Quantum object ordering

A system of this type is not holistic, but partially holistic, which means that pairwise interaction occurs between the holistic units. The distinction drawn here between holistic and partially holistic systems is not in line with the terminology used in general philosophic discourse and in order to avoid any confusion it is preferable to distinguish between systems that interact either continuously, or discontinuously, with the quantum potential field. Quantum potential, like the gravitational potential, occurs in the vacuum, presumably with constant intensity. The quantum potential energy of a quantum object therefore only depends on the wave function of the object. 

Once a set of quantum objects to study is chosen and the operator related to the MQSM definition in Eq. (2) is defined, the MQSM related to the set is unique. But they can be transformed or combined in order to obtain a new kind of auxiliary terms which can be named Quantum Similarity Indices (QSI). A vast quantity of possible MQSM manipulations leading to a variety of QSI definitions exists. The most used QSI are as follows. 

P3 A Quantum Object Set Ordering exists. In Section 6 it has been explained how an Object Set Ordering exists. This has been applied for several Quantum System examples in Section 9. It has been demonstrated how this ordering can be associated with the set by means of several techniques. 

Thus the quantum object set can be ordered at once when the CSIs, relating the quantum objects within the set, are known. Now, the immediate application of this ordering possibility may consist of the following procedure. Suppose that a property is known for quantum objects A and C 7tA 7tc. One will have either 7tA>irc or 7iA < 7ic. Any of such relationships permits obtaining an estimate of the supposedly unknown value of the property for the quantum object B, using the relationship (Eq. (3)), in either case as nA>nB>nc or nAupper bound for the value of the property for the quantum object B can easily be obtained from the knowledge of the similarity relationship (Eq. (3)). 

Density Functions play a fundamental role in the definition of Quantum Theory, due to this they are the basic materials used in order to define Quantum Objects and from this intermediate step, they constitute the support of Quantum Similarity Measures. Here, the connection of Wavefunctions with Extended Density Functions is analysed. Various products of this preliminary discussion are described, among others the concept of Kinetic Energy Distributions. Another discussed set of concepts, directly related with the present paper, is constituted by the Extended Hilbert Space definition, where their vectors are defined as column structures or diagonal matrices, containing both wavefunctions and their gradients. The shapes of new density distributions are described and analysed. All the steps above summarised are completed and illustrated, when possible, with practical application examples and visualisation pictures. 

The idea of Quantum Object (QO) without a well-designed formulation has been already used in the literature [30-32,35]. Moreover, the background mathematical structure leading towards the recently published [48,49] definition of QO is to be found within the possibility to construct a new kind of sets the Tagged Sets. In their definition, both set elements and known information on them are taken simultaneously into account. In order to obtain a sound QO definition, besides the definition of the Tagged Set concept [47], and furthermore to develop this line of thought, there are needed some preliminary considerations. 

Considerations relying on QS have been employed since the very beginning of its appearance as a potential source of ordering quantum objects, like MO s [67], conformers [68] or to find out properties of stereoisomers [69, 75]. However, one of the applications most used as time passed... 

Quantum physics makes similar pronouncements when it states that the electron is not somewhere or sometime it is a cloud of probabilities and that is all one can say about it. A similar quality adheres to my idea of time and the comparison of time to an object. If time is an object, then the obvious question to be asked is what is the smallest duration relevant to physical processes The scientific approach would be to keep dividing time into still smaller increments in order to find out if a discrete unit exists. What one is looking for by doing this is a chronon, or a particle of time. I believe the chronon exists, but it is not distinct from the atom. Atomic systems are chronons atoms are simply far more complicated than had been suspected. I believe that atoms have undescribed properties that can account not only for the properties of matter, but for the behavior of space/time as well. 

A gas in which the pressure no longer depends on the temperature is said to be degenerate, an unfortunate term indeed, because the corresponding state borders on perfection. One might call it a state of perfect fullness, since no interstice is left vacant. Electrons occupy all possible energy states and total order prevails. Both the electrical conductivity and the fluidity also attain perfection. Objects made from this sublime form of matter are perfectly spherical. And yet, in quantum circles, this state of nature is obstinately referred to as degenerate ... 

What is true is that, in any case, whether with the common microscope, or with the superresolution microscope, in order to be observed, the object points must be submitted to some kind of interaction. Since we are dealing with optical microscopes, the interaction occurs with photons. In such circumstances the photon, on interacting with the microparticle, is diffused by it. As a result of this interaction, which is fundamental in all direct concrete quantum measurements, a certain amount of momentum is transferred from the photon to the microparticle, leading to an uncertainty in the momentum of the microparticle. 

In order to discuss the group-theoretical formulation of quantum mechanics, which is the object of this section, we need to show that the infinitedimensional representation of the Heisenberg group ph(g) can be used as a basis for the vector space of hermitian operators [8]. 

The extravagent claims by which the new Quantum Mechanics was announced, are now largely forgotten, but not the belief that a new world order was established in science, free of concepts such as reality, causality, objectivity, certainty, predictability and many other notions based on classical views of the macroscopic world all of these to be replaced by statistical probabilities. 

---